Pentagon (EntityTopic, 12)

From Hi.gher. Space

(Difference between revisions)
(polytope explorer integration)
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| name=Pentagon
| name=Pentagon
| dim=2
| dim=2
-
| elements=5, 5
+
| elements=5 [[digon]]s, 5 [[point]]s
| genus=0
| genus=0
| ssc=G5
| ssc=G5
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| extra={{STS Matrix|
| extra={{STS Matrix|
  5 0
  5 0
-
  1 1}}{{STS Uniform polytope
+
  1 1}}{{STS Polytope
 +
| bowers=Peg
 +
| dual=''Self-dual''}}{{STS Uniform polytope
| schlaefli={5}
| schlaefli={5}
-
| vfigure=[[Digon]], length ?
+
| dynkin=x5o
-
| dual=''Self-dual''
+
| vfigure=[[Digon]], length (1+√5)/2
}}}}
}}}}
The '''pentagon''' can be seen as the two-dimensional analog to the [[dodecahedron]] in 3D and the [[cosmochoron]] in 4D. It is also the lowest-dimensional member of the [[ursatope]]s, with a (trivial) [[digon]]al base.
The '''pentagon''' can be seen as the two-dimensional analog to the [[dodecahedron]] in 3D and the [[cosmochoron]] in 4D. It is also the lowest-dimensional member of the [[ursatope]]s, with a (trivial) [[digon]]al base.

Revision as of 01:42, 26 March 2017

The pentagon can be seen as the two-dimensional analog to the dodecahedron in 3D and the cosmochoron in 4D. It is also the lowest-dimensional member of the ursatopes, with a (trivial) digonal base.

Equations

  • The hypervolumes of a pentagon with side length l are given by:
total edge length = 5l
area = 14 · √(25+10√5) · l2

Incidence matrix

Dual: Self-dual

#TXIDVaEaTypeName
0 Va= point ;
1 Ea2= digon ;
2 5a55= pentagon ;

Usage as facets


Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
Curved: circle